Gauge Covariance Relations and the Fermion Propagator in Maxwell-Chern-Simons QED3

TL;DR

This paper investigates the gauge covariance of the fermion propagator in Maxwell-Chern-Simons QED3, deriving a non-perturbative expression using LKFT and confirming its accuracy through one-loop calculations.

Contribution

It provides a non-perturbative gauge covariance relation for the fermion propagator in Maxwell-Chern-Simons QED3 using LKFT, extending previous results.

Findings

Perfect agreement with one-loop calculations in the weak coupling regime.

Reproduction of earlier results as special cases.

Derived a non-perturbative expression for the fermion propagator.

Abstract

We study the gauge covariance of the fermion propagator in Maxwell-Chern-Simons planar quantum electrodynamics (QED$_3$) considering four-component spinors with parity-even and parity-odd mass terms both for fermions and photons. Starting with its tree level expression in the Landau gauge, we derive a non perturbative expression for this propagator in an arbitrary covariant gauge by means of its Landau-Khalatnikov-Fradkin transformation (LKFT). We compare our findings in the weak coupling regime with the direct one-loop calculation of the two-point Green function and observe perfect agreement up to a gauge independent term. We also reproduce results derived in earlier works as special cases of our findings.